Understanding fixation processes and their probabilities is essential to the analysis of evolutionary games on finite populations. In this context, [1]} observed that even if individuals are interacting via the same game, the size \(N\)  of the population where they are included could lead to different evolutionarily stable strategies \(ESS_N\)  as defined in [2]}. This is an emerging feature of evolutionary processes under frequency-dependent fitness, since stability under the fixed fitness Moran process never depends on population size. Here, we provided an extensive analysis of the dependence of single mutant fixation probabilities on population size, focusing on the simplest \(2\times 2\)  games in well mixed populations.
